Question

The equation of a plane progressive harmonic wave is given as y = 3 sin [25pit-pi/2x] where x and y are in metre and t in second. The ratio of maximum particle velocity to the wave velocity?

Answer 1

$$\begin{gathered} y=3\sin \left[25\mathrm{\pi t}-\frac{\mathrm{\pi }}{2}\mathrm{x}\right] \\ y=3\sin \left[\omega t-kx\right] \\ \omega =25\pi ,k=\frac{\mathrm{\pi }}{2},A=3 \\ k=\frac{2\mathrm{\pi }}{\lambda }=\frac{\mathrm{\pi }}{2} \\ \lambda =4m \\ f=\frac{25\mathrm{\pi }}{2\mathrm{\pi }}=12.5Hz \\ c=f\lambda =12.5*4=50m/s \\ {v}_{max}=A\omega =3*25\pi =75\pi m/s \\ \frac{v_{max}}{c}=\frac{75\mathrm{\pi }}{50}=\frac{3\mathrm{\pi }}{2} \\ Regards \end{gathered}$$